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In the year 1905, a young Albert Einstein published a number of
scientific papers that changed physics forever. The best known of these,
the Special Theory of Relativity, quickly established the young Einstein as
a scientist of note (see J.IEI vol. 59:6) and led to Einsteins General Theory
of Relativity, one of the pillars of modern physics. In a second paper,
Einstein published a controversial proposal concerning the nature of light
that later formed a cornerstone of quantum theory, the revolutionary
theory that underpins much of modern science and technology (see J.IEI
vol. 59:7). Incredibly, the young Einstein made a third ground-breaking
advance in 1905.
He published an analysis that pointed the way towards a crucial test of
the reality of atoms, and of the validity of the laws of thermodynamics.
The outcome of that test now underpins much of modern science,
from our view of the atomic nature of matter to our understanding of
meteorology and other complex systems.
Atoms and chemistryThe idea that all matter is made up of minute, indivisible entities called
atoms was first put forward by the philosophers of ancient Greece. The
concept gained much credibility in the 19th century when scientists such
as John Dalton used it to establish laws of chemistry that successfully
described how the chemical elements combine to form molecules.
A listing of the known elements in order of increasing atomic
weight led to the development of The Periodic Table by Mendeleyev, a
development that revolutionized the study of chemistry. It was widely
assumed that the properties of a given element was determined by
the properties of its constituent atoms - however, there was no direct
evidence of the existence of atoms, and some eminent scientists did not
believe in the atomic hypothesis.
Enter EinsteinGreatly interested in the atomic view of matter, the young Einstein
devised a mathematical method of calculating the size of atoms and
molecules in early 1905. From an analysis of sugar molecules dissolved
in water, he calculated both the diameter of the sugar molecule and
Avogadros number (the number of molecules per unit volume under
standard conditions) from the known viscosity of the liquid and the
diffusion rate of sugar.
His calculations were in good agreement with previous theoretical
estimates and were well-received. However, the very existence of atoms
and molecules had still to be demonstrated in convincing fashion, and
the 26-year-old Einstein applied himself to this task.
Today, Einsteins notion of statistical fluctuations has found application throughout the sciences.
Einstein and statistics According to the atomic view of matter, a liquid is made up of a huge
number of molecules in random, ceaseless motion, the properties of the
liquid arising from the average behaviour of its constituent molecules.
Working from first principles, Einstein made a careful study of the
statistics of such an assembly and, in May 1905, he made a key proposal
concerning its behaviour.
He proposed that any such system would experience statistical
fluctuations, during which random elements depart from their average
behaviour (just as a dice player can occasionally throw several sixes in
a row).
Applying this concept of statistical fluctuation to the case of molecules
in liquids, Einstein proposed that a small group of neighbouring
Einstein and the Atomic Theory
Albert Einstein : another 1905 paper facilitated a test for atomic theory
In the third of a series of articles celebrating Einsteins Miraculous Year, Cormac ORaifeartaigh describes Einsteins ground-breaking contribution to atomic theory.
EINSTEIN
THE ENGINEERS JOURNAL vol. 59 : 8 October 2005
387
molecules could momentarily move in the same direction a fluctuation
that would cause a body immersed in the liquid to experience a tiny
push in that direction. Another group of molecules could cause the same
body to experience a tiny push in a different direction moments later and
the immersed body would therefore experience a zig-zag motion in the
liquid a motion that might be observable. Hence, while the molecules
of a liquid were far too small to be observed directly by microscope, their
motion might be detectable by its effect on a larger particle suspended
in the liquid!
Brownian MotionExcitingly, a zig-zag motion of particles suspended in a liquid had long
been known to scientists (named Brownian Motion after the English
botanist who studied the effect in detail). The cause of this motion had
been a great mystery and accurate measurement of the 3-D random
motion of an immersed particle had proved extremely difficult. Here,
Einstein made a second vital contribution.
Starting with the assumption that the motion was indeed due to a
buffeting of the immersed particle by the molecules of the liquid, he
calculated the average horizontal distance an immersed particle would
travel in a given time. Hence, from his own statistical analysis, Einstein
delivered a well-defined, measurable estimate that could be easily tested.
The experimentThe French scientist Jean Perrin rose to Einsteins challenge with a series
of experiments in 1908. Equipped with nothing but a microscope and
a stopwatch, Perrin and his team measured the horizontal displacement
of gum extract particles suspended in water as a function of time. The
data were in exact accord with Einsteins predictions, giving the world
the first unequivocal evidence of the reality of molecules. Einstein was
delighted, as was Perrin the Frenchman was later awarded the Nobel
Prize for this work!
Young Einstein devised a mathematical method of calculating the size of atoms and molecules in early 1905.
ImplicationsEinsteins Brownian-motion paper facilitated the first real glimpse
of the atomic nature of matter, an advance that underpins almost all
of modern science. Another consequence of the paper was that, since
the properties of matter were now known to be determined by the
behaviour of huge numbers of atoms, it was realized that the laws of
thermodynamics were valid only in a statistical sense.
For the first time, the role of probability in the laws of physics was
established, a defining moment in the philosophy of science.
Modern ApplicationsToday, Einsteins notion of statistical fluctuations has found application
throughout the sciences. From the study of cell membranes to our view
of evolution, from the analysis of weather systems to the study of the
stock market, it underpins our understanding of all complex systems.
Perhaps the Brownianmotion paper did not have quite the dramatic
impact of the Special Theory of Relativity, or indeed of Einsteins
quantum view of light but it resulted in a quiet revolution that has had
an lasting influence on modern science.
Dr Cormac ORaifeartaigh lectures in physics at Waterford Institute
of Technology
Above: Jean Perrin was awarded the 1926 Nobel Prize for his experimental verification of Einsteins predictions.
Left: The notion of statistical fluctuations underpins our view of complex systems such as the weather.
Brownian motion : the random motion of a particle suspended in a liquid was first studied by botanist Robert Brown (1773-1858).
Credit: NASA.
EINSTEIN
THE ENGINEERS JOURNAL vol. 59 : 8 October 2005